scholarly journals On the Intertranslatability of Argumentation Semantics

2011 ◽  
Vol 41 ◽  
pp. 445-475 ◽  
Author(s):  
W. Dvořák ◽  
S. Woltran
Keyword(s):  
Knowledge Representation ◽  
Abstract Argumentation ◽  
Negative Results ◽  
Complexity Results ◽  
Simple Formalism

Translations between different nonmonotonic formalisms always have been an important topic in the field, in particular to understand the knowledge-representation capabilities those formalisms offer. We provide such an investigation in terms of different semantics proposed for abstract argumentation frameworks, a nonmonotonic yet simple formalism which received increasing interest within the last decade. Although the properties of these different semantics are nowadays well understood, there are no explicit results about intertranslatability. We provide such translations wrt. different properties and also give a few novel complexity results which underlie some negative results.

scholarly journals Complexity of Abstract Argumentation under a Claim-Centric View

2019 ◽  
Vol 33 ◽  
pp. 2801-2808 ◽  
Author(s):  
Wolfgang Dvořák ◽  
Stefan Woltran
Keyword(s):  
Knowledge Base ◽  
Complexity Analysis ◽  
Decision Problems ◽  
Fixed Parameter Tractability ◽  
Abstract Argumentation ◽  
Complexity Results ◽  
Fixed Parameter

Abstract argumentation frameworks have been introduced by Dung as part of an argumentation process, where arguments and conflicts are derived from a given knowledge base. It is solely this relation between arguments that is then used in order to identify acceptable sets of arguments. A final step concerns the acceptance status of particular statements by reviewing the actual contents of the acceptable arguments. Complexity analysis of abstract argumentation so far has neglected this final step and is concerned with argument names instead of their contents, i.e. their claims. As we outline in this paper, this is not only a slight deviation but can lead to different complexity results. We, therefore, give a comprehensive complexity analysis of abstract argumentation under a claim-centric view and analyse the four main decision problems under seven popular semantics. In addition, we also address the complexity of common sub-classes and introduce novel parameterisations – which exploit the nature of claims explicitly – along with fixed-parameter tractability results.

scholarly journals Knowledge Representation in Probabilistic Spatio-Temporal Knowledge Bases

2016 ◽  
Vol 55 ◽  
pp. 743-798 ◽  
Author(s):  
Francesco Parisi ◽  
John Grant
Keyword(s):  
Knowledge Representation ◽  
Atomic Formula ◽  
Knowledge Bases ◽  
Integrity Constraints ◽  
Temporal Data ◽  
Complexity Results ◽  
Previous Definition ◽  
Spatio Temporal ◽  
Finite Domains

We represent knowledge as integrity constraints in a formalization of probabilistic spatio-temporal knowledge bases. We start by defining the syntax and semantics of a formalization called PST knowledge bases. This definition generalizes an earlier version, called SPOT, which is a declarative framework for the representation and processing of probabilistic spatio-temporal data where probability is represented as an interval because the exact value is unknown. We augment the previous definition by adding a type of non-atomic formula that expresses integrity constraints. The result is a highly expressive formalism for knowledge representation dealing with probabilistic spatio-temporal data. We obtain complexity results both for checking the consistency of PST knowledge bases and for answering queries in PST knowledge bases, and also specify tractable cases. All the domains in the PST framework are finite, but we extend our results also to arbitrarily large finite domains.

scholarly journals On Cycles, Attackers and Supporters --- A Contribution to The Investigation of Dynamics in Abstract Argumentation

2021 ◽  
Author(s):  
Ringo Baumann ◽  
Markus Ulbricht
Keyword(s):  
Knowledge Representation ◽  
Main Part ◽  
Research Area ◽  
Knowledge Representation And Reasoning ◽  
Major Research ◽  
Abstract Argumentation ◽  
Odd Cycle ◽  
The Impact ◽  
Odd Cycles

Abstract argumentation as defined by Dung in his seminal 1995 paper is by now a major research area in knowledge representation and reasoning. Dynamics of abstract argumentation frameworks (AFs) as well as syntactical consequences of semantical facts of them are the central issues of this paper. The first main part is engaged with the systematical study of the influence of attackers and supporters regarding the acceptability status of whole sets and/or single arguments. In particular, we investigate the impact of addition or removal of arguments, a line of research that has been around for more than a decade. Apart from entirely new results, we revisit, generalize and sum up similar results from the literature. To gain a comprehensive formal and intuitive understanding of the behavior of AFs we put special effort in comparing different kind of semantics. We concentrate on classical admissibility-based semantics and also give pointers to semantics based on naivity and weak admissibility, a recently introduced mediating approach. In the second main part we show how to infer syntactical information from semantical one. For instance, it is well-known that if a finite AF possesses no stable extension, then it has to contain an odd-cycle. In this paper, we even present a characterization of this issue. Moreover, we show that the change of the number of extensions if adding or removing an argument allows to conclude the existence of certain even or odd cycles in the considered AF without having further information.

Credulous and skeptical acceptability in probabilistic abstract argumentation: complexity results

2019 ◽  
Vol 12 (2) ◽  
pp. 181-191
Author(s):  
Bettina Fazzinga ◽  
Sergio Flesca ◽  
Filippo Furfaro
Keyword(s):  
Abstract Argumentation ◽  
Complexity Results

scholarly journals Probabilistic bipolar abstract argumentation frameworks: complexity results

2018 ◽  
Author(s):  
Bettina Fazzinga ◽  
Sergio Flesca ◽  
Filippo Furfaro
Keyword(s):  
Probabilistic Modeling ◽  
Deterministic Case ◽  
Abstract Argumentation ◽  
Complexity Results

Probabilistic Bipolar Abstract Argumentation Frameworks (prBAFs), combining the possibility of specifying supports between arguments with a probabilistic modeling of the uncertainty, are considered, and the complexity of the fundamentalproblem of computing extensions' probabilities is addressed.The most popular semantics of supports and extensions are considered, as well as different paradigms for defining the probabilistic encoding of the uncertainty.Interestingly, the presence of supports, which does not alter the complexity of verifying extensions in the deterministic case, is shown to introduce a new source of complexity in some probabilistic settings, for which tractable cases are also identified.

scholarly journals A General Notion of Equivalence for Abstract Argumentation

2017 ◽  
Author(s):  
Ringo Baumann ◽  
Wolfgang Dvořák ◽  
Thomas Linsbichler ◽  
Stefan Woltran
Keyword(s):  
General Notion ◽  
Abstract Argumentation ◽  
Complexity Results

We introduce a parametrized equivalence notion for abstract argumentation that subsumes standard and strong equivalence as corner cases. Under this notion, two argumentation frameworks are equivalent if they deliver the same extensions under any addition of arguments and attacks that do not affect a given set of core arguments. As we will see, this notion of equivalence nicely captures the concept of local simplifications. We provide exact characterizations and complexity results for deciding our new notion of equivalence.

scholarly journals Counting Complexity for Reasoning in Abstract Argumentation

2019 ◽  
Vol 33 ◽  
pp. 2827-2834 ◽  
Author(s):  
Johannes K. Fichte ◽  
Markus Hecher ◽  
Arne Meier
Keyword(s):  
Parameterized Complexity ◽  
Upper Bounds ◽  
Argumentation Framework ◽  
Bounded Treewidth ◽  
Abstract Argumentation ◽  
Counting Complexity ◽  
Complexity Results ◽  
Model Counting ◽  
Novel Algorithms ◽  
Input Instance

In this paper, we consider counting and projected model counting of extensions in abstract argumentation for various semantics. When asking for projected counts we are interested in counting the number of extensions of a given argumentation framework while multiple extensions that are identical when restricted to the projected arguments count as only one projected extension. We establish classical complexity results and parameterized complexity results when the problems are parameterized by treewidth of the undirected argumentation graph. To obtain upper bounds for counting projected extensions, we introduce novel algorithms that exploit small treewidth of the undirected argumentation graph of the input instance by dynamic programming (DP). Our algorithms run in time double or triple exponential in the treewidth depending on the considered semantics. Finally, we take the exponential time hypothesis (ETH) into account and establish lower bounds of bounded treewidth algorithms for counting extensions and projected extension.

scholarly journals If Nothing Is Accepted -- Repairing Argumentation Frameworks

2019 ◽  
Vol 66 ◽  
pp. 1099-1145
Author(s):  
Markus Ulbricht ◽  
Ringo Baumann
Keyword(s):  
Knowledge Representation ◽  
Knowledge Base ◽  
Search Space ◽  
Knowledge Representation And Reasoning ◽  
Hitting Set ◽  
Abstract Argumentation ◽  
Conflicting Information ◽  
All Solutions ◽  
First Results ◽  
Grounded Semantics

Conflicting information in an agent's knowledge base may lead to a semantical defect, that is, a situation where it is impossible to draw any plausible conclusion. Finding out the reasons for the observed inconsistency (so-called diagnoses) and/or restoring consistency in a certain minimal way (so-called repairs) are frequently occurring issues in knowledge representation and reasoning. In this article we provide a series of first results for these problems in the context of abstract argumentation theory regarding the two most important reasoning modes, namely credulous as well as sceptical acceptance. Our analysis includes the following problems regarding minimal repairs/diagnoses: existence, verification, computation of one and enumeration of all solutions. The latter problem is tackled with a version of the so-called hitting set duality first introduced by Raymond Reiter in 1987. It turns out that grounded semantics plays an outstanding role not only in terms of complexity, but also as a useful tool to reduce the search space for diagnoses regarding other semantics.

scholarly journals Complexity Results and Algorithms for Extension Enforcement in Abstract Argumentation

2017 ◽  
Vol 60 ◽  
pp. 1-40 ◽  
Author(s):  
Johannes P. Wallner ◽  
Andreas Niskanen ◽  
Matti Järvisalo
Keyword(s):  
Computational Complexity ◽  
Formal Model ◽  
Legal Reasoning ◽  
Knowledge Representation And Reasoning ◽  
Polynomial Hierarchy ◽  
Prototype System ◽  
Multi Agent Systems ◽  
Abstract Argumentation ◽  
Complexity Results ◽  
Complete Problems

Argumentation is an active area of modern artificial intelligence (AI) research, with connections to a range of fields, from computational complexity theory and knowledge representation and reasoning to philosophy and social sciences, as well as application-oriented work in domains such as legal reasoning, multi-agent systems, and decision support. Argumentation frameworks (AFs) of abstract argumentation have become the graph-based formal model of choice for many approaches to argumentation in AI, with semantics defining sets of jointly acceptable arguments, i.e., extensions. Understanding the dynamics of AFs has been recently recognized as an important topic in the study of argumentation in AI. In this work, we focus on the so-called extension enforcement problem in abstract argumentation as a recently proposed form of argumentation dynamics. We provide a nearly complete computational complexity map of argument-fixed extension enforcement under various major AF semantics, with results ranging from polynomial-time algorithms to completeness for the second level of the polynomial hierarchy. Complementing the complexity results, we propose algorithms for NP-hard extension enforcement based on constraint optimization under the maximum satisfiability (MaxSAT) paradigm. Going beyond NP, we propose novel MaxSAT-based counterexample-guided abstraction refinement procedures for the second-level complete problems and present empirical results on a prototype system constituting the first approach to extension enforcement in its generality.

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